Are quantum no-go theorems overrated/potentially counterproductive?

[bohm2]

Based on my own frustration with trying to reconcile the validity of some of the assumptions of the Von Newman, Bell's, Kochen-Specker, PBR theorem, etc., and other quantum no-go theorems, I thought these were some interesting papers critically discussing this topic:

In the area of the foundations of quantum mechanics a true industry appears to have developed in the last decades, with the aim of proving as many results as possible concerning what there cannot be in the quantum realm. In principle, the significance of proving ‘no-go’ results should consist in clarifying the fundamental structure of the theory, by pointing out a class of basic constraints that the theory itself is supposed to satisfy. In the present paper I will discuss some more recent no-go claims and I will argue against the deep significance of these results...

As we have seen, the supporters of the no-go strategy usually assume the extreme generality of their models as a virtue: we do not need to enter in too many details-they would probably argue-in order to show that we cannot extend orthodox quantum theory into a theory of quantum phenomena that preserves properties that some might like to retain-be they locality, realism, covariance or predictive power. The main point of the present paper is that that generality, far from being a virtue, is rather the opposite. It is exactly their being abstract and detached from the actual alternatives to quantum theory that deprives the proposed models proposed by the no-go strategies of a deeper significance. Not only do all these results take ordinary quantum theory itself at face value, so that the extending theories are supposed to inherit all the vagueness implicit in the orthodox treatment of the basic notions of ordinary quantum mechanics (clearly, the most urgent vagueness being the meaning of the wave function). But also the no-go results that we have discussed above, although addressing different issues, display an underlying common feature, that of avoiding any reference to a more detailed conceptual structure of the hypothetical theory that should extend or replace ordinary quantum theory.

Against the ‘No-Go’ Philosophy of Quantum Mechanics
http://philsci-archive.pitt.edu/100...antum_mechanics,_Revised_authored_version.pdf

Khrennikov arguing from a somewhat different perspective reaches a somewhat similar conclusion:

My decision to abandon HV was not a consequence of my better understanding of no-go theorems. (The better I understand them the more problems I see in their assumptions, especially in matching these assumptions to the real experimental situation...

I argue that, just as von Neumann’s “no-go” theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation.

The problem is that those who advance such arguments claim more than the known no-go theorems in fact imply. I cannot describe this situation better than Bell himself did: “long may Lois De Broglie continue to inspire those who suspect that what is proved by impossibility proofs is lack of imagination”

Bell argument: Locality or Realism? Time to make the choice.
http://arxiv.org/pdf/1108.0001.pdf

After my talk (May 3, 2004), I discussed with A. Leggett a role of no-go theorems in QM. In particular, I wondered why Einstein had never mentioned the von Neumann’s no-to theorem. (After Einstein’s death, the book of von Neumann was found in Einstein’s office.) A. Leggett remarked that Einstein was mainly interested in the real physical situation rather than in formal mathematical statements.

I found that all no-go statements contain some unphysical assumptions which are not valid for real experimental situations...

Vaxjo Interpretation of Wave Function: 2012
http://arxiv.org/pdf/1210.2390.pdf

 

[Demystifier]

I also think that it is more useful to construct models which DO reproduce predictions of quantum mechanics, then to prove general theorems telling what kind of theories can NOT do that.

For example, in Appendix A.1 of my recent paper
http://arxiv.org/abs/1309.0400
I explain how several no-go theorems/arguments against existence of relativistic-covariant version of Bohmian mechanics are circumvented by my own relativistic-covariant version of Bohmian mechanics.

 

[Jazzdude]

I too found no-go theorems to be very counter productive. I'm having a very hard time getting people to even look at my research results, because they "obviously violate some no-go theorems". They don't, because no-go theorems are always very limited to what exactly the author considered to be generally true. I tried to publish a paper showing a positive result, and it was rejected (without having been read) because they had published a no-go result just before. For me, no-go theorems and dogmatic prejudice go hand in hand.

Sorry for the little rant,

Jazz

 

[morrobay]

If a no go theorem is based on un realistic assumptions then it is counterproductive.
From the second paper referenced, Locality or Realism :
A realism assumption of pre existing measurement properties is incompatible with quantum
theory, independent from any derivation of an inequality.

 

[cgk]

I am not sure how useful this comment is, but if any of you would manage to create a theory reproducing quantum mechanical averages for n-particle systems[1], which is in some sense *computationally* favorable to wave function QM, you might find it easier to establish the theory indirectly via supporters in electronic structure theory, chemical dynamics, or similar fields. In such "applied quantum mechanics" fields, the main objective is generally obtaining predictions for concrete, realistic systems via approximations, and not the interpretation of fundamental QM. Since in any case many approximations are involved, people would be much more willing to adapt to new ways of doing things, if this allows for computing systems which are currently inaccessible.

[1] It is not even requires that correspondence is exact: It just needs to provide verifiably accurate approximations for a restricted, but known, class of problems.

 

[stevendaryl]

Based on my own frustration with trying to reconcile the validity of some of the assumptions of the Von Newman, Bell's, Kochen-Specker, PBR theorem, etc., and other quantum no-go theorems, I thought these were some interesting papers critically discussing this topic:

What has always struck me about Bell's theorem and various other no-go theorems is that they prove the impossibility of something that no mainstream physicists are trying to accomplish, anyway. The sort of hidden-variables theory that Bell proved was impossible is not a theory that anyone had seriously tried to develop, anyway.

 

[DrChinese]

Of course No-go theorems are powerful and useful. And of course they are constraining, to the frustration of many. That they are so often applied is a testament to their utility, and not dogmatism of the part of publications.

A good counter-example will blow away dogmatism, but please note the use of the adjective "good". So far, I have yet to see a good counter-example in any of the dozens of papers purporting same. And no, I don't read every one to "find" its flaw.

 

[Jazzdude]

Of course No-go theorems are powerful and useful. And of course they are constraining, to the frustration of many. That they are so often applied is a testament to their utility, and not dogmatism of the part of publications.

A good counter-example will blow away dogmatism, but please note the use of the adjective "good". So far, I have yet to see a good counter-example in any of the dozens of papers purporting same. And no, I don't read every one to "find" its flaw.

In an ideal world I would agree. I would've even agreed 5 years ago. What really happens is that people don't even bother to look at your arguments, so you don't even get to the point where they're evaluated. If you make bold enough claims and your paper is not just 2 pages, you can be pretty sure that nobody is going to read it until somebody else they trust read it and promoted it.

Physics is full of "practical" dogmatism these days. What is unlikely is not even considered, because it costs time. And this kind of subtle hostility towards new ideas is strongly supported by misunderstood or too broadly interpreted no-go theorems. And your formulation of "finding the flaw" fits this scheme perfectly. Instead of looking for flaws we should be looking for ideas.

Cheers,

Jazz

 

[Nugatory]

The sort of hidden-variables theory that Bell proved was impossible is not a theory that anyone had seriously tried to develop, anyway.

EPR weren't actively developing such a theory, but surely at the time that they published, pre-Bell, they believed that doing so would be a useful and important effort. Although we'll never know for sure, it's plausible that Einstein would have dropped this position if he had lived to see Bell's theorem.

Nonetheless, it would be an error to generalize from "Bell's no-go theorem is useful in guiding us away from unproductive investigations and for identifying the key experimental results that a candidate theory must predict" to "All no-go theorems are ..."

 

[Demystifier]

In an ideal world I would agree. I would've even agreed 5 years ago. What really happens is that people don't even bother to look at your arguments, so you don't even get to the point where they're evaluated. If you make bold enough claims and your paper is not just 2 pages, you can be pretty sure that nobody is going to read it until somebody else they trust read it and promoted it.

Physics is full of "practical" dogmatism these days. What is unlikely is not even considered, because it costs time. And this kind of subtle hostility towards new ideas is strongly supported by misunderstood or too broadly interpreted no-go theorems. And your formulation of "finding the flaw" fits this scheme perfectly. Instead of looking for flaws we should be looking for ideas.

Unfortunately, you are right. (Except that I don't think that 5 years ago the situation has been much different. Perhaps it was more like 50 years ago.)

 

[Jazzdude]

Unfortunately, you are right. (Except that I don't think that 5 years ago the situation has been much different. Perhaps it was more like 50 years ago.)

Yes, with the five years I was really referring to the moment when I realized it, not when it changed. I don't know if it was ever really different. There's a long history of brilliant new ideas being rejected and ridiculed at first, and often for a long time.

Cheers,

Jazz

 

[DrChinese]

Instead of looking for flaws we should be looking for ideas.

Cheers,

Jazz

Well, this is a statement much like "I want to end childhood hunger". Sounds great. We all wish our original ideas would be immediately recognized and accepted.

If only folks had looked at my last paper with a more open eye! It is ground-breaking...

 

[bhobba]

Unfortunately, you are right. (Except that I don't think that 5 years ago the situation has been much different. Perhaps it was more like 50 years ago.)

Yes, with the five years I was really referring to the moment when I realized it, not when it changed. I don't know if it was ever really different. There's a long history of brilliant new ideas being rejected and ridiculed at first, and often for a long time.

Yes that's true. The trouble is - what to do about it? All you can really do is try and be open minded - but aside from that it just seems to be one of those things associated with being human.

As far as the original question goes I believe no go theorems are very useful - not because what they imply is necessarily true - but disentangleing exactly what its saying can be very illuminating - eg Gleason's Theorem on the surface seems to rule out HV's - but understanding its assumption of non-contextuality is a valuable QM insight.

Thanks
Bill

 

[zonde]

In an ideal world I would agree. I would've even agreed 5 years ago. What really happens is that people don't even bother to look at your arguments, so you don't even get to the point where they're evaluated. If you make bold enough claims and your paper is not just 2 pages, you can be pretty sure that nobody is going to read it until somebody else they trust read it and promoted it.

It does not take many pages to say that you do not make assumptions used by no-go theorem. If you can't say in a couple of sentences why no-go theorem does not apply in your situation it would be quite sound reason to stop reading further.

Instead of looking for flaws we should be looking for ideas.

I personally favour looking for flaws. However not the ones DrChinese is talking about.


Speaking about utility of no-go theorems - their utility is not in increasing our knowledge about physical reality. They rather help to increase consistency of our ideas.

 

[Jazzdude]

It does not take many pages to say that you do not make assumptions used by no-go theorem. If you can't say in a couple of sentences why no-go theorem does not apply in your situation it would be quite sound reason to stop reading further.

It's not quite that simple. You can easily state that the usual no-go theorems do not apply. But usually the exact reason how that works is quite complicated, because otherwise it would be rather obvious and you wouldn't have to write a paper about it. In the end it's not unlikely that the entire point of the paper is to explain why the no-go theorem does not apply, so you're back where you started: To get people to actually read the paper.

I personally favour looking for flaws. However not the ones DrChinese is talking about.

Sometimes looking for flaws is helpful, in order to gain understanding. But if someone comes up with a new idea, looking for flaws is counter productive, because usually what you think is a flaw and an actual misunderstanding of what is being argued are indistinguishable. So the first objective should be to really try to understand the idea as presented by the author, before looking for errors. In my experience the "obvious error" often is on the side of the reader.

Speaking about utility of no-go theorems - their utility is not in increasing our knowledge about physical reality. They rather help to increase consistency of our ideas.

Yes, no-go theorems are useful. But like I said earlier they can support dogmatism. Especially if they're used as short cuts for actual thinking. I've seen no-go theorem being misapplied in discussions very often, and it took a lot of effort to set this straight, turning the whole discussion into a one about the understanding of those theorems instead of being constructive.

Cheers,

Jazz

 

[Demystifier]

Yes, no-go theorems are useful. But like I said earlier they can support dogmatism. Especially if they're used as short cuts for actual thinking. I've seen no-go theorem being misapplied in discussions very often, and it took a lot of effort to set this straight, turning the whole discussion into a one about the understanding of those theorems instead of being constructive.

I agree. One of the reasons is the following. No-go theorems usually have the form:
If conditions C1, C2, ..., Cn are fulfilled, then A is not possible.
The problem is that people tend to forget the conditions, and remember only that A is not possible.

 

[bhobba]

The problem is that people tend to forget the conditions, and remember only that A is not possible.

Yes - but we have the cautionary tale of Von Neumann's proof.

He didn't explicitly state the assumption he made about the linearity of expectation values and considering his reputation people simply accepted it. A few people pointed it out but were generally ignored.

It wasn't until Bell took up the baton it really became well known.

My view is it behooves all of us to be careful - but as sure as death and taxes we will fail - but must try.

Thanks
Bill

 

[stevendaryl]

Yes - but we have the cautionary tale of Von Neumann's proof.

He didn't explicitly state the assumption he made about the linearity of expectation values and considering his reputation people simply accepted it. A few people pointed it out but were generally ignored.

It wasn't until Bell took up the baton it really became well known.

My view is it behooves all of us to be careful - but as sure as death and taxes we will fail - but must try.

Thanks
Bill

Almost nothing in physics is conclusively proved impossible. But at some point, a consensus develops that certain ideas are not worth pursuing further. Whether that's good or bad is an open question. There are always more possible lines of inquiry than there are researchers to pursue them.

 

[zonde]

It's not quite that simple. You can easily state that the usual no-go theorems do not apply. But usually the exact reason how that works is quite complicated, because otherwise it would be rather obvious and you wouldn't have to write a paper about it. In the end it's not unlikely that the entire point of the paper is to explain why the no-go theorem does not apply, so you're back where you started: To get people to actually read the paper.

Hmm, are you sure it's related to no-go theorems? Have you other experience with another paper that does not involved no-go theorems and when it was easy to get people to read the paper? Maybe it's rather your argumentation skills. Look what you wrote:

Sometimes looking for flaws is helpful, in order to gain understanding. But if someone comes up with a new idea, looking for flaws is counter productive, because usually what you think is a flaw and an actual misunderstanding of what is being argued are indistinguishable. So the first objective should be to really try to understand the idea as presented by the author, before looking for errors. In my experience the "obvious error" often is on the side of the reader.

A lot of hand waving without any solid argument. But if I try to understand your idea without paying attention to poor arguments (I should judge new ideas by how they improve my understanding) it turns out that your idea is still no better - a lot of effort but result is still the same.

Yes, no-go theorems are useful. But like I said earlier they can support dogmatism. Especially if they're used as short cuts for actual thinking. I've seen no-go theorem being misapplied in discussions very often, and it took a lot of effort to set this straight, turning the whole discussion into a one about the understanding of those theorems instead of being constructive.

Yes you said that no-go theorems can support dogmatism. But you are not telling why. You can misapply ordinary theorems too - this is not an argument.

 

[strangerep]

Maybe it's rather [one's] argumentation skills. [...]

I must agree with that. A wise man told me some time ago that if an author cannot express themselves clearly and concisely, they probably have nothing valuable to say anyway, and the effort of trying to follow their paper is likely a waste.

You could call that wisdom a "no-go" theorem, for which I have yet to find a counter example.

 

[bohm2]

As an example of stuff that confuses me about no-go theorems, consider the recent PBR theorem:

At one extreme, there's some like Antony Valentini calling the PBR theorem as the most important advance in the field since Bell’s inequality. At the other extremes, other papers have labelled it "garbage and anti-quantum-mechanics”.

Some of the criticism relates to some of the assumptions of PBR theorem, particularly that:

Systems prepared independently have independent physical states.

Just as the no-go result of the Bell–Kochen–Specker theorem has taught us about the failure of noncontextuality for quantum measurements, we suggest one can learn an important lesson from the PBR theorem about the failure of separability in ontological models.

Is the Pusey–Barrett–Rudolph Theorem Compatible with Quantum Nonseparability?
http://arxiv.org/pdf/1306.5805v1.pdf

One of the PBR authors (Jonathan Barrett) just published today another paper seemingly discussing this criticism:

The theorem, however, considers only models in which the physical variables corresponding to independently prepared systems are independent. This work considers models that are defined for a single quantum system of dimension d, such that the independence condition does not arise.

No ψ-epistemic model can fully explain the indistinguishability of quantum states
http://arxiv.org/pdf/1310.8302.pdf

It seems Jonathan Barrett takes this PBR assumption more seriously than the other co-author (Terry Rudolph) who writes that the key assumption is preparation independence (no conspiracy/superdeterminism) just like in Bell's theorem:

Let me briefly explain the interesting science that lies at the heart of the “key assumption” the editor is alluding to in the above. I will call this assumption preparation independence. Suppose an experiment at one lab reproduces the results of an earlier experiment at another. This would righty be called an “independent” verification of the first lab’s results. No scientist would attempt to refute this by appealing to correlations between random events at the two labs, there being no realistic mechanism for such to be established. Even in a single lab, repeated runs of an experiment must be assumed independent in order to estimate probabilities based on the results. Preparation independence is simply the assumption that we have the ability to build independent, uncorrelated experimental apparatuses to act as preparation devices of microscopic systems, and that any deeper theory of nature than quantum theory will not overthrow this principle by virtue of “hidden super-correlations” where to date scientists have always successfully assumed there are none.

The theorem we prove – that quantum states cannot be understood as merely lack of knowledge of an underlying deeper reality described by some as yet undiscovered deeper theory – assumes preparation independence. It is an important insight that this assumption is necessary for the theorem, and the point of our second paper was to show this explicitly. That second paper is, however, simply making a mathematical/logical point – it is not a serious proposal for how the physical world operates..

Guest Post: Terry Rudolph on Nature versus Nurture
http://www.preposterousuniverse.com...-post-terry-rudolph-on-nature-versus-nurture/

This back and forth claims and counterclaims is all very confusing and I'm not sure if any real insights have been made?

 

[bhobba]

At one extreme, there's some like Antony Valentini calling the PBR theorem as the most important advance in the field since Bell’s inequality. At the other extremes, other papers have labelled it "garbage and anti-quantum-mechanics”.

In any endeavor its not uncommon to find experts disagreeing. If the issue concerns you there is no way out except the long hard slog of learning the details yourself and making up you own mind.

Post here if you want to discuss it with others - but in the end you have to decide.

It took me years of study on my own to get to where I am with QM - and am still learning. Its a long hard slog - but really its the only way.

Thanks
Bill

 

[zonde]

This back and forth claims and counterclaims is all very confusing and I'm not sure if any real insights have been made?

I can only repeat what I said in post #14:
Speaking about utility of no-go theorems - their utility is not in increasing our knowledge about physical reality. They rather help to increase consistency of our ideas.

But to gain consistency you have to sort it out. In your particular example, what has more weight - scientific method with all the knowledge that is developed by using it or particular interpretation of QM? :uhh:

 

[audioloop]

In an ideal world I would agree. I would've even agreed 5 years ago. What really happens is that people don't even bother to look at your arguments, so you don't even get to the point where they're evaluated. If you make bold enough claims and your paper is not just 2 pages, you can be pretty sure that nobody is going to read it until somebody else they trust read it and promoted it.

Physics is full of "practical" dogmatism these days. What is unlikely is not even considered, because it costs time. And this kind of subtle hostility towards new ideas is strongly supported by misunderstood or too broadly interpreted no-go theorems. And your formulation of "finding the flaw" fits this scheme perfectly. Instead of looking for flaws we should be looking for ideas.

Cheers,

Jazz

great words.


.

 

[naima]

one of the most surprising no go theorem comes from Haag. He says that interaction picture does not exist.

 

[bohm2]

But to gain consistency you have to sort it out. In your particular example, what has more weight - scientific method with all the knowledge that is developed by using it or particular interpretation of QM? :uhh:

I'm not sure if the two can be separated at least with respect to QM? For instance some like E.T. Jaynes writes:

Our present quantum mechanical formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature-all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that this unscrambling is a pre-requisite for any further advance in basic physical theory

I guess I see this as being important; unfortunately it's not clear that no-go theorems, at least up to this point, have made any progress in this direction. This is especially given that there is so much disagreement on the implications and validity of the premises of many of these no-go theorems. Maybe this is to be expected at the limits of human knowledge but it's frustrating when there's so much contradiction/disagreement.

 

[Maui]

Because of the weird rules of quantum theory, it's much easier to show how the world is not than how the world is. That's all.

 

[zonde]

I'm not sure if the two can be separated at least with respect to QM?

Not sure I understand. In your post you was talking about PBR and whether "key assumption" of preparation independence can be relaxed or no.
I just say that I agree with Terry Rudolph here:
http://www.preposterousuniverse.com...-post-terry-rudolph-on-nature-versus-nurture/
saying that you can't relax this "key assumption" without leaving realm of scientific inquiry.

 

[bohm2]

Not sure I understand. In your post you was talking about PBR and whether "key assumption" of preparation independence can be relaxed or no.
I just say that I agree with Terry Rudolph here:
http://www.preposterousuniverse.com...-post-terry-rudolph-on-nature-versus-nurture/
saying that you can't relax this "key assumption" without leaving realm of scientific inquiry.

But is it clear that is the meaning of the key assumption? In the last paragraph of the other link I provided, those authors don't appear to interpret it that way when they write:

Just as the no-go result of the Bell–Kochen–Specker theorem [6, 7] has taught us about the failure of noncontextuality for quantum measurements, we suggest one can learn an important lesson from the PBR theorem about the failure of separability in ontological models. Namely, even for a quantum tensor-product state, physical states” sufficient to model measurements on a composite system may not be determined just by “real physical states” associated with the separate components.

When PBR first came out, Demystifier had contacted one of the authors (Barrett) and pointed out something that seems very similar:
https://www.physicsforums.com/showpost.php?p=3627144&postcount=95
https://www.physicsforums.com/showpost.php?p=3628836&postcount=123
https://www.physicsforums.com/showpost.php?p=3628847&postcount=124

Rob Spekkens makes a seemingly similar point in this abstract of his lecture:

This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program. I will review the evidence in favour of the psi-epistemic approach and describe the pre-existing reasons for thinking that if a quantum state represents knowledge about reality then it is not reality as we know it, i.e., it is not the kind of reality that is posited in the standard hidden variable framework. I will argue that the PBR theorem provides additional clues for "what has to give" in the hidden variable framework rather than providing a reason to retreat from the psi-epistemic position... The connection between the PBR theorem and other no-go results will be discussed. In particular, I will point out how the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory, regardless of the status of separability (though not in the form posited by PBR). I will also consider the connection of PBR to the failure of local causality by considering an experimental scenario which is in a sense a time-inversion of the PBR scenario.

Why I Am Not a Psi-ontologist
http://pirsa.org/displayFlash.php?id=12050021

So I'm not sure if it's clear that the key assumption is as is interpreted by Terry Rudolph? See also this thread discussing some of these points/difficulties:

Do Bell and PBR together point toward nonlocal reality?
https://www.physicsforums.com/showthread.php?t=695354&highlight=Barrett

Note that even Demystifier's point regarding Bell's (e.g. that Bell's theorem-and its variations suggests that either locality or reality is wrong) is universally accepted. There are some physicists that have argued that it implies non-locality irrespective of 'realism' issues:

What do violations of Bell's inequalities tell us about nature?
https://www.physicsforums.com/showthread.php?t=670856

In particular, Norsen, Gisin, Maudlin, Goldstein, etc. taking the latter view with respect to violation of Bell's argue that:

...the role of Bell’s theorem is not to set constraints on how ‘realist’ we are allowed to be about quantum systems but rather, much more interestingly, to characterize a structural property of any theory that aims to cover the domain of validity covered so far by quantum mechanics, namely non-locality. As a consequence, whether a theory aiming to supersede quantum theory will be ‘realist’, ‘non-realist’, ‘half-realist’ or ‘one-third realist’, this will concern the further conceptual and formal resources of that theory and not at all the Bell theorem

Non-Local Realistic Theories and the Scope of the Bell Theorem
http://arxiv.org/ftp/arxiv/papers/0811/0811.2862.pdf

This is what is so confusing about no-go theorems. The disagreement continues after so many years. Perhaps, it's because it's far more difficult to show/prove non-existence (evidence of absence)?

 

[audioloop]

it's because it's far more difficult to show/prove non-existence (evidence of absence)?

indeed.
how can an absence create a non-absence ?
from nothing (a no-reality a reality) create something ?
.

 

[bhobba]

Bohm2 quoted E.T. Jaynes:
'Our present quantum mechanical formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature-all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that this unscrambling is a pre-requisite for any further advance in basic physical theory'

I most emphatically do NOT agree with that at all. As Ballentine shows it follows from 2 axioms - and to a certain extent the second axiom follows from the first via Gleasons theorem so its really wrapped up in one axiom.

And that axiom has a reasonable justification that goes something like this:

Imagine we have a system and some observational apparatus that has n possible outcomes associated with values yi. This immediately suggests a vector and to bring this out I will write it as Ʃ yi |bi>. Now we have a problem - the |bi> are freely chosen - they are simply man made things that follow from a theorem on vector spaces - fundamental physics can not depend on that. To get around it QM replaces the |bi> by |bi><bi| to give the operator Ʃ yi |bi><bi| - which is basis independent. This is the foundational axiom of QM, and heuristically why its reasonable.

IMHO it is not a mismash of ideas, it is the consequence of one key and very fundamental idea.

What it means is another issue - and that is hotly debated.

But what the theory says, and even why it says it, is IMHO VERY well understood - what it MEANS is what's discussed.

This is what I mean by you really need to read the modern texts on QM like Ballentine that develops it correctly from the modern perspective, then make up your own mind - you will not get it from the commentary of those that may have a different view than what you would form, and may not have even been exposed to the modern approach detailed in Ballentine. I find it VERY hard to believe Jaynes could have a view like that after being exposed to a modern treatment - my understanding is he died in 1998 and his views were probably formed from the early textbooks like Dirac and Von Neumann - things have moved on considerably since then.

In my early exposure to QM I learned it from those two texts - the treatment of Ballentine a WAY WAY ahead of those - but that's only to be expected - we have had many decades of research separating them.

Thanks
Bill

 

[bohm2]

I most emphatically do NOT agree with that at all. As Ballentine shows it follows from 2 axioms - and to a certain extent the second axiom follows from the first via Gleasons theorem so its really wrapped up in one axiom.

The quote of Jaynes which you disagree with came from the original PBR paper (see first page):

On the reality of the quantum state
http://arxiv.org/pdf/1111.3328.pdf

If you don't favour realist interpretation of quantum states, then PBR has no implications. Epistemic interpretations of the quantum state can be divided into 2 types:

1. those that are epistemic with respect to underlying ontic states
2. those that are epistemic with respect to measurement outcomes

The PBR theorem (with the few assumptions noted below) would place serious constraints on 1. but not 2. As far as I understand it, Ballentine's view (I've read only a few chapters of his book but not all of it) is sympathetic to the ensemble interpretation. I don't know much about it, but PBR just rules out certain realist interpretations (e.g. Einstein's). The diagram attached (from The life of psi article) below nicely summarizes the 4 major positions:

But again the PBR no-go theorem makes the following assumptions:

1. a system has a "real physical state" not necessarily completely described by quantum theory, but objective and independent of the observer
2. systems that are prepared independently have independent physical states

If one's interpretation doesn't make those assumptions, PBR is irrelevant.

 

[bhobba]

If you don't favour realist interpretation of quantum states, then PBR has no implications. Epistemic interpretations of the quantum state can be divided into 2 types:

This has nothing to do with interpretation - it has to do with the formalism of QM - which is what the quote you gave referred to:

'Our present quantum mechanical formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature-all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that this unscrambling is a pre-requisite for any further advance in basic physical theory'

Every physicist agrees with the formalism. And while it may not have been true when the person that was quoted studied QM, nowadays we know that only two axioms are required to derive all of QM. And if you accept Gleason's theorem then you only need one. Most definitely the formalism of QM is NOT a mishmash of ideas - it is the logical development of a very fundamental idea. The exact idea depending on exactly what approach you use. In my approach its basis independence. Other approaches are based on reasonableness conditions imposed on generalized probability models eg:
http://arxiv.org/pdf/quant-ph/0101012.pdf

There are probably others as well. But the point remains the same. The formalism is well understood. Interpreting it is another matter.

Thanks
Bill

 

[Demystifier]

one of the most surprising no go theorem comes from Haag. He says that interaction picture does not exist.

The theorem is valid only for quantum field theory, which has an INFINITE number of degrees of freedom and thus leads to UV and IR divergences. If you regularize the theory such that UV and IR divergences are removed (which you always must do to make sense of interacting QFT), then the Haag theorem does not longer apply and the interaction picture exists.

For details, see also the book
A. Duncan, The Conceptual Framework of Quantum Field Theory (2012)

 

[bohm2]

This has nothing to do with interpretation - it has to do with the formalism of QM - which is what the quote you gave referred to...

Okay, but it is the latter part of that quote that I was referring to. We are discussing physical theories. On its own, the QM formalism is just a piece of mathematics. There is little agreement on interpretation and unscrambling and this is important. Whether no-go theorems have made any advance in this direction is what I'm questioning.

Zonde had argued (if I understand him) that one of the PBR assumptions should not be questioned (e.g. systems that are prepared independently have independent physical states), because without it, we would have to abandon the scientific method. But I'm still confused if that PBR assumption actually implies this? Some physicists suggest it does (e.g. T. Rudolph). Others (e.g. Spekkens) argue that it just hi-lites the necessary separability/contextuality of QM. What is confusing is that 2 recent experiments have been done questioning the ψ-epistemic interpretation but they do rely on the assumptions noted above:

If systems have real states, regardless of an experimenter or measurements performed, then a natural question is whether the quantum state is epistemic, i.e. corresponding merely to knowledge of these underlying real states. In the presented manuscript we tested for this specific possibility and ruled out the most natural class of such models to a high degree of confidence.

Can different quantum state vectors correspond to the same physical state? An experimental test
http://arxiv.org/pdf/1211.0942v1.pdf

Assuming a natural continuity assumption and a separability assumption, we show here that epistemic interpretations of the quantum state are in contradiction with quantum theory...Our experimental results are in agreement with the predictions of quantum theory and provide strong constraints on possible epistemic extensions of quantum mechanics..

Experimentally probing the reality of the quantum state
http://arxiv-web3.library.cornell.edu/pdf/1211.1179v1.pdf